The number x is rational. Which statement about sqrt 13 - x is true? Choices: (A)sqrt 13 - x is rational. (B)sqrt 13 - x is irrational. (C)sqrt 13 - x can be rational or irrational, depending on the value of x.

Identify Type of Number: Identify whether sqrt(13) is a rational or irrational number. 13 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. Therefore, sqrt(13) is an irrational number.Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational. Since x is rational and sqrt(13) is irrational, their difference, sqrt(13) - x, must be irrational.Verify with Example: Verify the statement with an example. Let x be a rational number, for example, x = 1. Then sqrt(13) - x = sqrt(13) - 1. Since sqrt(13) is irrational, subtracting 1 (a rational number) from it cannot result in a rational number. Therefore, sqrt(13) - x is irrational.

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The number $x$ is rational. Which statement about $\sqrt{13} - x$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{13} - x$ is rational. $\newline$ (B) $\sqrt{13} - x$ is irrational. $\newline$ (C) $\sqrt{13} - x$ can be rational or irrational, depending on the value of $x$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

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Q. The number

x

is rational. Which statement about

\sqrt{13} - x

is true?

\newline

Choices:

\newline

(A)

\sqrt{13} - x

is rational.

\newline

(B)

\sqrt{13} - x

is irrational.

\newline

(C)

\sqrt{13} - x

can be rational or irrational, depending on the value of

x

Identify Type of Number: Identify whether $\sqrt{13}$ is a rational or irrational number. $13$ is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. Therefore, $\sqrt{13}$ is an irrational number.
Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational. Since $x$ is rational and $\sqrt{13}$ is irrational, their difference, $\sqrt{13} - x$ , must be irrational.
Verify with Example: Verify the statement with an example. $\newline$ Let $x$ be a rational number, for example, $x = 1$ . $\newline$ Then $\sqrt{13} - x = \sqrt{13} - 1$ . $\newline$ Since $\sqrt{13}$ is irrational, subtracting $1$ (a rational number) from it cannot result in a rational number. $\newline$ Therefore, $\sqrt{13} - x$ is irrational.